What is the (dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200 ?

The (dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200 is -0.032P+2

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(dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200

\frac{d P}{d t} = 0.16 P (1 - \frac{P}{1000}) - 30, P (0) = 200

- 0.032 P + 2

Solution steps

Find

0.16 P (1 - \frac{P}{1000}) - 30

given

P (0) = 200

0.16 P (1 - \frac{P}{1000}) - 30 = 0.16 P (1 - \frac{P}{1000}) - 30

P : 200

\frac{P}{1000} : \frac{200}{1000}

= 0.16 \cdot 200 (1 - \frac{P}{1000}) - 30

Expand

0.16 \cdot 200 (1 - \frac{P}{1000}) - 30 : - 0.032 P + 2

= - 0.032 P + 2

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What is the (dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200 ?
The (dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200 is -0.032P+2